Question

What is the instantaneous velocity of an object with position at time t equal to `f(t)= ((t-2)^3,sqrt(5t-3))` at `t=2`?

Answer 1

Instantaneous velocity, at t = 2 is `5/14sqrt7=0.9449`, nearly, in (distance)/(time) units.

Explanation:

Velocity

`= f'(t)`

`=sqrt((x')^2+(y')^2)`

`=sqrt(9(t-2)^4+25/4(1/(5t-3))`

`=sqrt(0+25/4(1/7))`, at t = 2

`=5/14sqrt7`